Details

sample149.0ms

Algorithm

intervals

Results

49.0ms	118×	body	160	valid
46.0ms	225×	body	80	nan
33.0ms	138×	body	80	valid

simplify864.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

864.0ms

(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize31.0ms

Local error

Found 4 expressions with local error:

10.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(* (/ t l) (/ t l))
0.2b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
96×	`times-frac`
72×	`*-un-lft-identity`
69×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
21×	`sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 179

Calls

4 calls:

Slowest

25.0ms	(* (/ t l) (/ t l))
18.0ms	(* (/ Om Omc) (/ Om Omc))
7.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
37.0ms	(* (/ t l) (/ t l))
35.0ms	(* (/ Om Omc) (/ Om Omc))
11.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify10.4s

Counts

187 → 191

Calls

187 calls:

Slowest

498.0ms	(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
411.0ms	(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
291.0ms	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
290.0ms	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
276.0ms	(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.5b

localize32.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.3b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(* (/ t l) (/ t l))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
125×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
93×	`add-cube-cbrt`
65×	`sqrt-prod`
30×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
14×	`difference-of-squares`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
6×	`associate-/r*` `sqrt-div`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `flip3-+` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `associate-/l/`
1×	`rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 232

Calls

4 calls:

Slowest

20.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
15.0ms	(* (/ t l) (/ t l))
12.0ms	(* (/ Om Omc) (/ Om Omc))
3.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
63.0ms	(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
48.0ms	(* (/ Om Omc) (/ Om Omc))
28.0ms	(* (/ t l) (/ t l))

simplify28.0s

Counts

285 → 244

Calls

285 calls:

Slowest

562.0ms	(* (/ (* (* Om Om) Om) (* (* Omc Omc) Omc)) (* (* (/ Om Omc) (/ Om Omc)) (/ Om Omc)))
457.0ms	(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
420.0ms	(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
420.0ms	(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
402.0ms	(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))

prune3.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize54.0ms

Local error

Found 4 expressions with local error:

10.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.2b	(* (/ Om Omc) (/ Om Omc))
0.2b	(* (/ t l) (/ t l))
0.2b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
96×	`times-frac`
72×	`*-un-lft-identity`
69×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
21×	`sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 179

Calls

4 calls:

Slowest

17.0ms	(* (/ t l) (/ t l))
14.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
13.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
43.0ms	(* (/ t l) (/ t l))
41.0ms	(* (/ Om Omc) (/ Om Omc))
11.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify10.1s

Counts

187 → 191

Calls

187 calls:

Slowest

413.0ms	(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
394.0ms	(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
285.0ms	(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
283.0ms	(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
281.0ms	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize56.0ms

Local error

Found 4 expressions with local error:

10.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
0.6b	(/ 2 (* (/ l t) (/ l t)))
0.3b	(* (/ l t) (/ l t))
0.2b	(* (/ Om Omc) (/ Om Omc))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
103×	`add-sqr-sqrt`
86×	`*-un-lft-identity`
72×	`add-cube-cbrt`
46×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
19×	`pow1`
17×	`cbrt-undiv` `div-exp`
12×	`prod-exp` `cbrt-unprod`
10×	`div-inv`
8×	`difference-of-squares` `unswap-sqr`
5×	`associate-/r/` `distribute-lft-out`
4×	`insert-posit16` `add-log-exp`
3×	`frac-times` `associate-l/` `associate-r/` `associate-/l*`
2×	`pow2` `rem-sqrt-square` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 206

Calls

4 calls:

Slowest

50.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
26.0ms	(/ 2 (* (/ l t) (/ l t)))
23.0ms	(* (/ l t) (/ l t))
15.0ms	(* (/ Om Omc) (/ Om Omc))

series265.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
48.0ms	(/ 2 (* (/ l t) (/ l t)))
44.0ms	(* (/ Om Omc) (/ Om Omc))
43.0ms	(* (/ l t) (/ l t))

simplify13.1s

Counts

212 → 218

Calls

212 calls:

Slowest

453.0ms	(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
448.0ms	(* (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))) (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))))
390.0ms	(* (/ (sqrt Om) (sqrt Omc)) (sqrt (/ Om Omc)))
381.0ms	(/ (* (* 2 2) 2) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))
359.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (- (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (* 1 1))))

prune2.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.1b

regimes476.0ms

Accuracy

98.7% (0.1b remaining)

Error of 5.3b against oracle of 5.2b and baseline of 10.2b

bsearch13.0ms

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.6s	3723×	body	160	valid
1.6s	8009×	body	80	nan
1.4s	4277×	body	80	valid